Finite Group Databasebeta

← #14755257

Subgroups — #14755257

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623350C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4#13077061C211yesmaximal, characteristic, complemented
5#13068980C218yesmaximal, complemented
6C2×#10622197C211yesmaximal, characteristic, complemented
7#13068342C211yesmaximal, characteristic, complemented
8C2×C11×#575C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C11×#575—22no—
12C11×#575—22no—
13C11×#575C414yescomplemented
14C11×#575C2214yes—
15C2×C11×#137—21no—
16C2×C11×#137C412yescomplemented
17C2×C11×AGL(1,ℤ/8)—21no—
18C2×C11×AGL(1,ℤ/8)C412yescomplemented
19C2×C11×#135—22no—
20C22×C11×M16C2211yescharacteristic
21#10623350—22no—
22#10623350—22no—
23#10623350—22no—
24#10623350C2214yescomplemented
25C2×#67001—22no—
26C2×#67001—22no—
27C2×#66979C2211yescharacteristic
28C22×#4318—22no—
29C22×#4318C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622849—22no—
33#10622849C2214yescomplemented
34C2×#66901—22no—
35#10622847—22no—
36#10622847C2214yescomplemented
37#10622846C2214yescomplemented
38#10622845—22no—
39#10622838—21no—
40#10622828—21no—
41#10622820—22no—
42#10622197C2214yescomplemented
43#10622196C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41C2×C412yes—
61C2×C11×#41C2×C412yes—
62C2×C11×#41C2×C412yes—
63C2×C11×#41D412yes—
64C2×C11×#41D412yes—
65C2×C11×#41D412yes—
66C2×C11×#41C2312yes—
67C2×C11×#41C2312yes—
68C22×Q8×C11C2×C411yescharacteristic
69C22×Q8×C11D411yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11C2×C411yescharacteristic
73C22×D4×C11D411yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C11×#137—24no—
78C11×#137—24no—
79C11×#137—24no—
80C11×#137C2×C418yescomplemented
81C11×AGL(1,ℤ/8)—24no—
82C11×AGL(1,ℤ/8)—24no—
83C11×AGL(1,ℤ/8)—24no—
84C11×AGL(1,ℤ/8)C2×C418yescomplemented
85C11×#135—28no—
86C11×#135—28no—
87C2×C11×Q16—22no—
88C2×C11×SD16—22no—
89C2×C11×SD16—22no—
90C2×C11×D8—22no—
91C2×C11×M16—21no—
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16C2×C412yes—
95C2×C11×M16C2×C412yes—
96C2×C11×M16C2312yes—
97C22×C8×C11—21no—
98C2×C22⋊Dic11—21no—
99#67001—28no—
100#67001—28no—
101#67001—28no—
102#67001—28no—
103#66979—21no—
104#66979—21no—
105#66979—21no—
106#66979C2312yes—
107C2×C4⋊Dic11—21no—
108C2×C4×Dic11—21no—
109C2×#4318—24no—
110C2×#4318—28no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—21no—
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318—28no—
119C2×#4318—21no—
120C2×#4318—21no—
121C2×#4318—21no—
122C2×#4318—21no—
123C2×#4318—21no—
124C2×#4318—21no—
125C2×#4318D412yes—
126C2×#4318D412yes—
127C2×#4318D412yes—
128C2×#4318C2312yes—
129C2×#4318C2312yes—
130C22×C11⋊C8—24no—
131C22×C11⋊C8—21no—
132C22×C11⋊C8D412yes—
133C22×C11⋊C8C2312yes—
134#66901—28no—
135#66899—24no—
136#66896—24no—
137C22⋊(C11⋊C8)—28no—
138#20939—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11#4111yescharacteristic
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—22no—
155C11×#41—22no—
156C11×#41—22no—
157C11×#41—22no—
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—41no—
163C11×#41—41no—
164C11×#41—41no—
165C11×#41—41no—
166C11×#41—41no—
167C11×#41—41no—
168C11×#41—41no—
169C11×#41—41no—
170C11×#41C22⋊C414yes—
171C11×#41C22⋊C414yes—
172C11×#41C22×C414yes—
173C11×#41C2×D414yes—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11C22⋊C412yes—
183C2×Q8×C11C22⋊C412yes—
184C2×Q8×C11C22×C412yes—
185C2×Q8×C11C2×D412yes—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—41no—
203C2×D4×C11—41no—
204C2×D4×C11—41no—
205C2×D4×C11—41no—
206C2×D4×C11C22⋊C412yes—
207C2×D4×C11C22⋊C412yes—
208C2×D4×C11C22×C412yes—
209C2×D4×C11C2×D412yes—
210C22×C4×C11—21no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—41no—
221C22×C4×C11—41no—
222C22×C4×C11—41no—
223C22×C4×C11—41no—
224C22×C4×C11C22×C411yescharacteristic
225C22×C4×C11C22×C411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11#4111yescharacteristic
235C22×C4×C11#4111yescharacteristic
236C22×C4×C11#4111yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C22×Dic11—41no—
239C11×Q16—28no—
240C11×SD16—28no—
241C11×SD16—28no—
242C11×D8—28no—
243C11×M16—22no—
244C11×M16—22no—
245C11×M16—22no—
246C11×M16C22×C414yes—
247C2×C8×C11—22no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C22⋊Dic11—22no—
251C22⋊Dic11—41no—
252C4⋊Dic11—22no—
253C4⋊Dic11—41no—
254C4×Dic11—22no—
255C4×Dic11—41no—
256#4318—216no—
257#4318—22no—
258#4318—22no—
259#4318—22no—
260#4318—22no—
261#4318—22no—
262#4318—22no—
263#4318—22no—
264#4318—41no—
265#4318—41no—
266#4318—41no—
267#4318—41no—
268#4318C2×D414yes—
269C2×C11⋊C8—216no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2×D414yes—
279C2×#575D1111yescharacteristic
280C2×#568—111no—
281C2×#421—111no—
282#2896—111no—
283#2879—111no—
284#1881—118no—
285C2×#344—111no—
286#1738—111no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—81no—
294C23×C11—82no—
295C23×C11—82no—
296C23×C11C4×D411yescharacteristic
297C23×C11C4×D411yescharacteristic
298C23×C11#12111yescharacteristic
299C23×C11#12111yescharacteristic
300C23×C11#12311yescharacteristic
301C23×C11#12311yescharacteristic
302C23×C11C2×#4111yescharacteristic
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—41no—
309Q8×C11—41no—
310Q8×C11C2×C22⋊C414yes—
311D4×C11—24no—
312D4×C11—24no—
313D4×C11—24no—
314D4×C11—24no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—42no—
321D4×C11—42no—
322D4×C11—42no—
323D4×C11—42no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11C2×C22⋊C414yes—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—24no—
333C2×C4×C11—24no—
334C2×C4×C11—22no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C2×C22⋊C411yescharacteristic
342C2×C4×C11C2×C22⋊C411yescharacteristic
343C2×C4×C11C2×C22⋊C411yescharacteristic
344C2×C4×C11C2×C22⋊C411yescharacteristic
345C2×C4×C11C4×D411yescharacteristic
346C2×C4×C11C4×D411yescharacteristic
347C2×C4×C11C4×D411yescharacteristic
348C2×C4×C11C4×D411yescharacteristic
349C2×C4×C11C4×D411yescharacteristic
350C2×C4×C11C4×D411yescharacteristic
351C2×C4×C11#12011yescharacteristic
352C2×C4×C11#12011yescharacteristic
353C2×C4×C11#12011yescharacteristic
354C2×C4×C11#12011yescharacteristic
355C2×C4×C11#12111yescharacteristic
356C2×C4×C11#12111yescharacteristic
357C2×C4×C11#12111yescharacteristic
358C2×C4×C11#12111yescharacteristic
359C2×C4×C11#12111yescharacteristic
360C2×C4×C11#12111yescharacteristic
361C2×C4×C11#12311yescharacteristic
362C2×C4×C11#12311yescharacteristic
363C2×C4×C11C23×C411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×Dic11—42no—
370C2×Dic11—82no—
371C8×C11—24no—
372C11⋊C8—24no—
373C11⋊C8—24no—
374C11⋊C8—42no—
375C22×#41C2×D1111yescharacteristic
376C22×#41C2×D1111yescharacteristic
377#575—22no—
378#575—22no—
379#575Dic1114yescomplemented
380#575C2×D1114yes—
381C2×#137—21no—
382C2×#137Dic1112yescomplemented
383C2×AGL(1,ℤ/8)—21no—
384C2×AGL(1,ℤ/8)Dic1112yescomplemented
385C2×#135—22no—
386#568—114no—
387#568—222no—
388#568—222no—
389#568—222no—
390C2×#131—222no—
391C2×#131—222no—
392C22×M16—111no—
393C22×M16—111no—
394C22×M16—111no—
395C22×M16—222no—
396C22×M16C2×D1111yescharacteristic
397C2×#117—111no—
398#421—114no—
399#421—222no—
400C2×#104—222no—
401#419—221no—
402#418—221no—
403#417—222no—
404#416—114no—
405#408—114no—
406#408—222no—
407#407—222no—
408#344—114no—
409#341—114no—
410C22×C11—24no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—44no—
419C22×C11—44no—
420C22×C11—42no—
421C22×C11—82no—
422C22×C11—82no—
423C22×C11—82no—
424C22×C11—82no—
425C22×C11#38611yescharacteristic
426C22×C11#38611yescharacteristic
427C22×C11#38611yescharacteristic
428C22×C11#38611yescharacteristic
429C22×C11C2×C4×D411yescharacteristic
430C22×C11C2×#12111yescharacteristic
431C22×C11C2×#12311yescharacteristic
432C4×C11—24no—
433C4×C11—42no—
434C4×C11#38611yescharacteristic
435C4×C11#38611yescharacteristic
436C4×C11#38611yescharacteristic
437C4×C11#38611yescharacteristic
438C4×C11C22×C22⋊C411yescharacteristic
439C4×C11C2×C4×D411yescharacteristic
440C4×C11C2×#12011yescharacteristic
441C4×C11C2×#12111yescharacteristic
442Dic11—82no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×Dic1112yes—
460C2×#41C2×Dic1112yes—
461C2×#41C2×Dic1112yes—
462C2×#41C22⋊D1112yes—
463C2×#41C22⋊D1112yes—
464C2×#41C22⋊D1112yes—
465C2×#41C22×D1112yes—
466C2×#41C22×D1112yes—
467C22×Q8C2×Dic1111yescharacteristic
468C22×Q8C22⋊D1111yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4C2×Dic1111yescharacteristic
472C22×D4C22⋊D1111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4C22×D1111yescharacteristic
476#137—24no—
477#137—24no—
478#137—24no—
479#137C2×Dic1118yescomplemented
480AGL(1,ℤ/8)—24no—
481AGL(1,ℤ/8)—24no—
482AGL(1,ℤ/8)—24no—
483AGL(1,ℤ/8)C2×Dic1118yescomplemented
484#135—28no—
485#135—28no—
486C2×Q16—22no—
487C2×SD16—22no—
488C2×SD16—22no—
489C2×D8—22no—
490#131—228no—
491#131—228no—
492#131—228no—
493#131—228no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—112no—
498C2×M16—112no—
499C2×M16—112no—
500C2×M16—112no—
501C2×M16—112no—
502C2×M16—228no—
503C2×M16—224no—
504C2×M16—228no—
505C2×M16—221no—
506C2×M16—221no—
507C2×M16—221no—
508C2×M16—221no—
509C2×M16—221no—
510C2×M16—221no—
511C2×M16—221no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—221no—
515C2×M16—221no—
516C2×M16—221no—
517C2×M16—221no—
518C2×M16C2×Dic1112yes—
519C2×M16C2×Dic1112yes—
520C2×M16C22×D1112yes—
521C22×C8—21no—
522C22×C8—112no—
523C22×C8—112no—
524C22×C8—224no—
525C22×C8—221no—
526#117—112no—
527#117—221no—
528#117—221no—
529#117—221no—
530C2×C4⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C42—221no—
533#104—228no—
534#103—224no—
535#102—224no—
536C22⋊C8—228no—
537C2×C11—21no—
538C2×C11—21no—
539C2×C11—21no—
540C2×C11—21no—
541C2×C11—21no—
542C2×C11—21no—
543C2×C11—21no—
544C2×C11—44no—
545C2×C11—82no—
546C2×C11C2×#38611yescharacteristic
547C24—21no—
548C24—21no—
549C24#434111yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41C22⋊Dic1114yes—
579#41C22⋊Dic1114yes—
580#41C22×Dic1114yes—
581#41C2×C22⋊D1114yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8C22⋊Dic1112yes—
591C2×Q8C22⋊Dic1112yes—
592C2×Q8C22×Dic1112yes—
593C2×Q8C2×C22⋊D1112yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4C22⋊Dic1112yes—
615C2×D4C22⋊Dic1112yes—
616C2×D4C22×Dic1112yes—
617C2×D4C2×C22⋊D1112yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—441no—
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4D4×D1111yescharacteristic
637C22×C4#434111yescharacteristic
638C22×C4#434111yescharacteristic
639C22×C4#434111yescharacteristic
640C22×C4C22×Dic1111yescharacteristic
641C22×C4C22×Dic1111yescharacteristic
642C22×C4C2×C22⋊D1111yescharacteristic
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C23×D1111yescharacteristic
647Q16—28no—
648SD16—28no—
649SD16—28no—
650D8—28no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—114no—
655M16—2216no—
656M16—222no—
657M16—222no—
658M16—222no—
659M16—222no—
660M16—222no—
661M16—222no—
662M16—222no—
663M16—441no—
664M16—441no—
665M16—441no—
666M16—441no—
667M16C22×Dic1114yes—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—114no—
672C2×C8—2216no—
673C2×C8—222no—
674C2×C8—222no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8—222no—
678C2×C8—222no—
679C2×C8—222no—
680C2×C8—222no—
681C4⋊C4—222no—
682C4⋊C4—441no—
683C22⋊C4—222no—
684C22⋊C4—441no—
685C42—222no—
686C42—441no—
687C11#2093911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—82no—
696C23—82no—
697C23D4×Dic1111yescharacteristic
698C23D4×Dic1111yescharacteristic
699C23#6698811yescharacteristic
700C23#6698811yescharacteristic
701C23#6699211yescharacteristic
702C23#6699211yescharacteristic
703C23C2×#434111yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8C2×C22⋊Dic1114yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4C2×C22⋊Dic1114yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—442no—
743C2×C4—882no—
744C2×C4D4×Dic1111yescharacteristic
745C2×C4D4×Dic1111yescharacteristic
746C2×C4D4×Dic1111yescharacteristic
747C2×C4D4×Dic1111yescharacteristic
748C2×C4D4×Dic1111yescharacteristic
749C2×C4D4×Dic1111yescharacteristic
750C2×C4#6698811yescharacteristic
751C2×C4#6698811yescharacteristic
752C2×C4#6699011yescharacteristic
753C2×C4#6699011yescharacteristic
754C2×C4#6699011yescharacteristic
755C2×C4#6699011yescharacteristic
756C2×C4#6699211yescharacteristic
757C2×C4#6699211yescharacteristic
758C2×C4#6699211yescharacteristic
759C2×C4#6699211yescharacteristic
760C2×C4#6699211yescharacteristic
761C2×C4#6699211yescharacteristic
762C2×C4C2×C22⋊Dic1111yescharacteristic
763C2×C4C2×C22⋊Dic1111yescharacteristic
764C2×C4C2×C22⋊Dic1111yescharacteristic
765C2×C4C2×C22⋊Dic1111yescharacteristic
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C2×C4C2×#434111yescharacteristic
769C2×C4C23×Dic1111yescharacteristic
770C2×C4C22×C22⋊D1111yescharacteristic
771C2×C4C22×C22⋊D1111yescharacteristic
772C8—24no—
773C8—224no—
774C8—224no—
775C8—442no—
776C22—24no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22#1062283311yescharacteristic
792C22#1062283311yescharacteristic
793C22#1062283311yescharacteristic
794C22#1062283311yescharacteristic
795C22C2×D4×Dic1111yescharacteristic
796C22C2×#6698811yescharacteristic
797C22C2×#6699211yescharacteristic
798C4—24no—
799C4—42no—
800C4—882no—
801C4#1062283311yescharacteristic
802C4#1062283311yescharacteristic
803C4#1062283311yescharacteristic
804C4#1062283311yescharacteristic
805C4C2×D4×Dic1111yescharacteristic
806C4C2×#6699011yescharacteristic
807C4C2×#6699211yescharacteristic
808C4C22×C22⋊Dic1111yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—44no—
817C2—82no—
818C2C2×#1062283311yescharacteristic
subgroupG/H
centerC4C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#575C2
socleC2×C11C2×#386
cosocleC22×C4×C11C24
hypercenterC2×#575D11
hypocenterC11#20939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623350C2semidirect
2. C2×#10622849C2semidirect
3. #13077135C2semidirect
4. #13077061C2semidirect
5. #13068980C2semidirect
6. C2×#10622197C2semidirect
7. #13068342C2semidirect
13. C11×#575C4semidirect
16. C2×C11×#137C4semidirect
18. C2×C11×AGL(1,ℤ/8)C4semidirect
24. #10623350C22semidirect
33. #10622849C22semidirect
36. #10622847C22semidirect
37. #10622846C22semidirect
42. #10622197C22semidirect
43. #10622196C22semidirect
80. C11×#137C2×C4semidirect
84. C11×AGL(1,ℤ/8)C2×C4semidirect
379. #575Dic11semidirect
382. C2×#137Dic11semidirect
384. C2×AGL(1,ℤ/8)Dic11semidirect
479. #137C2×Dic11semidirect
483. AGL(1,ℤ/8)C2×Dic11semidirect
687. C11#20939semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233502
C2×#106228492
#130771352
#130770612
#130689802
C2×#106221972
#130683422
C2×C11×#5752
#2093911